Consider a spring mass system with following parameter.m = 1, c = 4, k = 5, force = e-3* cos 2xFind the transient motion of the system assuming that it is initially at rest state. Show the detailsof your work.

Write the general expression of the spring-mass system. Ft=md2xdt2+cdxdt+k Substitute m=1, c=4,…

Consider a spring mass system with following parameter. m = 1,c = 4, k = 5, force -3x = e cos 2x Find the transient motion of the system assuming that it is initially at rest state. Show the details of your work.

Consider a spring mass system with following parameter. m = 1,c = 4, k = 5, force -3x = e cos 2x Find the transient motion of the system assuming that it is initially at rest state. Show the details of your work.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Related questions

Q: 3.22. For the system shown in Fig. P3.11, derive the differential equation of motion for small…

Q: The mass equals 1 kg, the spring constant equals 25 N/m, and the damping coefficient equals 0.05…

Q: Find the motion of the system in the figure below with mass 0.25 kg, no damping, spring constant 1…

A: Write the differential equation of motion.…

Q: Consider a SDOF system having a mass m = 30 kN s2 /m, damping c = 50 kNs/m and stiffness k = 4000…

A: given; mass(m)=30*1000kgdamping coefficient(c)=50*1000Ns/mstiffness of…

Q: 20. Spring Theory. One end of a spring with spring constant k = 6.50N /m is connected to a ball of…

A: Given: The spring constant, k = 6.5 N/m The mass of the ball, m = 5 kg The initial length of the…

Q: Consider a spring-mass-damper system with k = 4000 N /m, m = 10 kg, and e = 40 N.s/m. Find the…

Q: 30 kg.m2 The figure below shows a single degree of freedom control surface/actuator system. The…

A: Given Data The mass moment of inertia is:J=30 kg·m2 The spring stifness is:k=3000 N/m The damping…

Q: Q.5 A 6-kg uniform cylinder of radius 50 cm can roll without sliding on a horizontal surface and is…

Q: mass ! hangs on the end of a cord around a pulley of radius 5 and moment of inertia 6, rotating with…

Q: A mass-spring-dashpot system with constants k = 0,6, c = 0,7 and 0 g makes mechanical vibration. The…

Q: A mass of 3kg stretches a spring from its naturał length of 8.3°cm; to a length of 13,2cm.The mass…

Q: weight of mass 2 kg is placed on a long vertical spring with spring constant k = 20. The damping…

Q: A body of mass 14 kg is suspended vertically on a spring and stretches it 49 cm. At t=0, the mass is…

Q: Example: A 16 lb weight stretches a spring 1.6 ft. At the equilibriumposition, the weight is given a…

Q: 2. A 3 kg object is attached to spring and will stretch the spring 392 mm by itself. There is no…

Q: Q3) A 16 Ib cylinder stretches a spring 2/27 inches by itself. The spring is initially displaced 1/2…

Q: Q3) A 16 lb cylinder stretches a spring 2/27 inches by itself. The spring is initially displaced 1/2…

A: according to the given data

Q: A 75 N bar is rotating downward at 2 rad/s. The spring has an unstretched length of 2 m and a spring…

Q: A mass weighing 96 Ib is attached to a spring hanging from the ceiling and comes to rest at its…

A: m=96 lbs F(t)=3 cos 6t lbs k=15 lb/ft c=2 lb-sec/ft g=32 ft/sec2 Now, ωn=1596ωn2=0.15625 and,…

Q: Two identical pendulums, each with mass m and length I, are connected by a spring of stiff- ness k…

Q: Q) The system show in Figure has a block weight= 20 N, stiffness = 2000 N/m, damped coefficient = 20…

Q: the equivalent spring constant for below if the constant spring is 80 ?N/m 1/11 k1 m3 k3 k6 m1 k4 m2…

Q: : Nrite down the differential equation(s) that model the vertical dynamics of the system below…

A: dear student please rate me postive :) Stay safe stay happy ! data given - A system with two mass…

Q: Q4: - Using Laplace transforms to Find the displacement equation of mass (3 kg) attached with three…

Q: (a) the system is underdamped with ξ = 0.09, (b) the system is critically damped; and (c) the system…

A: GIven: m = 0.5 kg, l = 0.5 m, a = 0.2 m, and k = 3000 N/m To determine: Damping coefficient (a)the…

Q: The system shown in Fig. P3.3 consists of a uniform rod which has length 1, mass m, and mass moment…

A: Given: The mass of the rod is m, the length of the rod is l, and the mass moment of inertia about…

Q: The physical system shown below consists of a mass, viscous damping, and two parallel springs. Do…

Q: A mass weighing 12N stretches a spring 0.5m. The mass is attached to a viscous damper with a damping…

Q: 3.22. For the system shown in Fig. P3.11, derive the differential equation of motion for small…

Q: A simple harmonic oscillator, of mass m and natural frequency wo, experiences an oscillating driving…

A: Write the expression of motion. d2xdt2+ω02x=acosωt

Q: The mechanical cnergy of an idcal mass-spring system is constant as kinctic energy converts to…

A: Given:

Q: Q2/ A (5 kg) block is attached to a spring of spring constant (500 Nm". It slides without friction…

A: Springs are one of the flexible machine elements, which gets deformed when load is applied to it and…

Q: 8. A mass of 1 kg is attached to a spring hanging vertically from the ceiling. Suppose the damping…

A: Weight of an object can be determined as mass times the acceleration due to gravity. The force…

Q: A vibratory system consists of a mass 12,5 kg, a spring of stiffness 1000 N/m, and a dashpot with…

A: Given:mass, m=12.5 kgspring stiffness, k=1000 N/mdamping coefficient, c=15 N-s/m

Q: Consider a typical viscously damped spring-mass system, as shown in figure P4 below, for which the…

A: f

Q: Consider a driven oscialting spring-mass system modeled by my' '+ by' + ky = F, cos(wt). Find the…

Q: A spring has a mass of 10 kg, is underdamped with coefficient β = 5 and its frequency is 0.8 Hz.…

Q: Consider the damped mass-spring system for mass of 1.5 kg, spring constant 10 N/m, lamping 3 kg/s…

Q: A single-story building frame is subjected to a harmonic ground acceleration as shown in Figure 7.…

Q: A 0.1 kg object oscillates as a simple harmonic motion along the x-axis with a frequency f =3.185…

A: We need to use basic equations of vibration to solve this question...

Q: Consider the mass-spring system shown in the figure below. Assume the natural frequency of the…

A: Given: ωn=10 rad/sFo=0.3 mω = 2ωnxo=10 mmvo=30 mm/st = 24 s

Q: Q2|\ For the System shown in figure determine 1. Equation of Motion 2. Find the response of the…

Q: An undamped spring/mass system, in which m = 8 slugs and the spring constant k = 16 lb/ft has a…

A: Suppose 0< t < π=2. Consider the diagram below, where P is the point (cos( t ) ;sin(t)) on the…

Q: A 0.31kg block rest on a orizonal surface and is attached to a spring (constant=41 N/m ). The block…

Q: For the system shown in figure below, derive the differential equation of motion for small…

Q: Find the velocity of a free vibration with a response of 4(d^2 x/dt^2) + 25x = o when t = 2.5s.…

Q: What is the step response of the dynamic system pictured below?

A: The equation of motion for the system for spring 2, b1xo˙-y˙+k2xo=0b1xo+k2xo˙=b1y˙…

Q: (a) The position of a mass in a spring-mass system is given as x(t) = 2cos4t. Find the period of…

Concept explainers

Forced undamped vibrations

In mechanical engineering, vibration is expressed as the term that occurs due to an object's backward and forward movement about a point of equilibrium. Generally, there are three types of vibrations which are,

Question

Consider a spring mass system with following parameter.
m = 1, c = 4, k = 5, force = e-3* cos 2x
Find the transient motion of the system assuming that it is initially at rest state. Show the details
of your work.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

Suppose a mass-spring system has spring constant 712 N/m and mass 4.4 kg. The mass is displaced in the negative x-direction by 0.22 m and set in motion at 2.55 m/s in the positive x-direction. Calculate the phase shift as a positive angle in radians, assuming a cosine solution.
the pump and motor assembly stops work when you find the sum of the product of vibration intensity and acceleration, the speed, and twice the product of vibration intensity and distance moved. Derive the homogenous differential equation for this situation, then determine the series solution for this equation, using Leibnitz-Maclaurin method.
A helical spring has spring constant k. If the wire diameter, spring diameter and the number of coils are all doubled then the spring constant of the new spring becomes
Q4/ For the figure below the spring is used to stop a 10 kg package. If the maximum deflection in the spring is 70 mm, (a) the total work of the system in the figure below is: 8m/s H=0,25 /K=400N/m 10kg 500m 0-30 (b): The total work when theta =0 equal to: *
A model for forced spring mass system is given by: my" + cy' + ky=r(t) (i) Find the steady state solution (y,) for case with value of m= 1, c=4, k= 4 and r(t) = 2cost (ii) Find the solution (y.Y, ) that satisfies y(0) =1 and y '(0) =2
Find the period and make a graph of "xv/s t", of a mass-spring system with elastic constant K=8 Kg/s² and m=2 Kg, which moves from its equilibrium position ma, distance d = 0.5m . Make a graph of damped and undamped.
2- Two mass-spring systems A & B both have stiffness of k-10 N/m. The mass of system A is twice the mass of system B (mA=2mg= 1 kg), which system will oscillate faster? Why? Support your answer with a plot.
4. Consider a mass of 500 g placed at the end of a spring with stiffness constant 100 N/m and hanging at rest. The mass is displaced downward by 1.0 cm and released from rest. When the motion sets in, a time-varying force F(t) = cos³ 2t is applied to the spring-mass system. Solve the nonhomogeneous 2nd order differential equation representing the motion. That is, solve for x(t). [Note: Take the downward direction as the negative x-axis.]
For the following mechanical systems, obtain the equations of motion in Laplace domain.
F(1) Spring m. Ball Dashpot Find the motion of the mass-spring system with the driving force F(t) shown above for the given data. [Hint: Read Forced Oscillations notes.] e-2t, 0 2 y(0) = 1, y'(0) =-1.5.
A:YA Q2.pdf > Q) The system show in Figure has a block weight= 20 N, stiffness = 2000 N/m, damped coefficient = 20 N.s/m, r =10 cm and I= 0.2 kg. m. The harmonic force is effected on the blocked mass with F(t)= F sin wt, where F= 100 N and w=10 rad/s. Find the equation of motion to the system, natural frequency, damped ratio and damped natural frequency. 2r ww f(t) C
Find the equation of motion using the Lagrangian method?